CS216: Program and Data Representation University of Virginia Computer Science Spring 2006 David Evans Lecture 1: Introduction

2 UVa CS216 Spring Lecture 1: Analyzing Algorithms Menu Motivating Problem Course Structure, Expectations, Goals Analyzing Algorithms

3 UVa CS216 Spring Lecture 1: Analyzing Algorithms Phylogeny from

4 UVa CS216 Spring Lecture 1: Analyzing Algorithms Language Phylogeny tree house baum haus treow hus tre hus strom domovni arbol casa albero casa arbore casa arbre maison Latin: arbor domus casa

5 UVa CS216 Spring Lecture 1: Analyzing Algorithms Language Phylogeny English German Anglo-Saxon Norwegian Czech Spanish Italian Romanian French

6 UVa CS216 Spring Lecture 1: Analyzing Algorithms Tree of Life From

7 UVa CS216 Spring Lecture 1: Analyzing Algorithms Finding a Phylogeny Speculate on history based on current evidence –Not guaranteed to be correct Find the “most likely” history –Parsimony: find the evolutionary tree that explains the observations with the fewest possible changes

8 UVa CS216 Spring Lecture 1: Analyzing Algorithms Measuring Changes Natural Languages –Grammatical Rules –Lexicon –Hard to quantify how similar two languages are Species –Genomes (only recently) –Easy to quantify: genome differences are measurable

9 UVa CS216 Spring Lecture 1: Analyzing Algorithms How Species Evolve Point Mutations (Substitution): one base is replaced with another …CAT… …CTT… UV Ray With only point mutations, easy to tell how close two genomes are, just count the different bases

10 UVa CS216 Spring Lecture 1: Analyzing Algorithms How Species Evolve 2 Insertions: one or more bases are inserted Deletions: one or more bases are removed …GCATG… …GCACATG… …GCATCATG… …GCATG… Caused by copying errors (enzymes slipping, etc.)

11 UVa CS216 Spring Lecture 1: Analyzing Algorithms Measuring Genome Similarity Insertions and Deletions this hard ACATCATCATCAT CATCATCATCATC are more “similar” than ACATCATCATCAT | | | | TCGTTCGCGAAAA

12 UVa CS216 Spring Lecture 1: Analyzing Algorithms Sequence Alignment Align sequences by inserting gaps: Find best alignment inserting gaps given: –value of matching bases (point mutations) = c –cost of a gap (insertion/deletion) = g ACATCATCATCAT |||||||||||| -CATCATCATCAT We use c = 10, g = 2 : goodness = 12 * c – g = 118

13 UVa CS216 Spring Lecture 1: Analyzing Algorithms Brute Force Alignment To find the best alignment of sequences U and V with correct value c and gap penalty g: if U or V is empty U, V is the best alignment otherwise, [ next slide ]

14 UVa CS216 Spring Lecture 1: Analyzing Algorithms Brute Force Alignment: Otherwise… Try three possibilities: 1. First elements of U and V are aligned: score of best alignments of U[1:] and V[1:] + c if U[0] == V[0] 2. First element of U is aligned with a gap in V score of best alignments of U[1:] and V + g 3. First element of V is aligned with a gap in U score of best alignments of U and V[1:] + g Pick the choice with the highest score U[1:] means U with the first element removed

15 UVa CS216 Spring Lecture 1: Analyzing Algorithms Is this a “good” solution?

16 UVa CS216 Spring Lecture 1: Analyzing Algorithms Course Structure, Expectations, Goals

17 UVa CS216 Spring Lecture 1: Analyzing Algorithms Staff Me: David Evans (Call me “Dave” or “Coach”) –Office Hours posted on course website –Always available by , if I don’t reply in 24 hours, send again and complain Assistant Coaches: Erika Chin, David Faulkner, Erin Golub, Sam Guarnieri, Katherine Jogerst, and Pitchaya (“Yam”) Sitthi-Amorn –Will lead Monday and Tuesday sections –Available in Small Hall lab at posted times (only)

18 UVa CS216 Spring Lecture 1: Analyzing Algorithms Meetings Lectures: 2 per week –Will include material not in the book –Most lectures will use slides and notes Section meetings: 1 per week –You must sign up for one of the sections –Classroom work, group exercises, review, quizzes, … Staffed time in Small Hall –Take advantage of help from the ACs and your classmates

19 UVa CS216 Spring Lecture 1: Analyzing Algorithms Problem Sets 8 total, 1-2½ weeks each Work on them when and where you want (but take advantage of staffed lab time in Small Hall) Usually will work with partners Mix of programming and analysis Main way most will learn Turn in on paper at beginning of class (first is due Wednesday)

20 UVa CS216 Spring Lecture 1: Analyzing Algorithms My Teaching Philosophy: Drinking from a Firehose It may hurt a little bit, and a lot of water will go by you, but you won’t go away thirsty! Don’t be overwhelmed! You will do fine.

21 UVa CS216 Spring Lecture 1: Analyzing Algorithms Expectations: Programming Background You understand basic programming: –Can write a program longer than a screenful –Can understand multi-file programs –Familiar with common control structures, procedures, recursive definitions You don’t freak out when you are expected to learn a new language on your own

22 UVa CS216 Spring Lecture 1: Analyzing Algorithms Expectations: Math and Logic Background You remember some things from CS202 (or will learn/re-learn them when you need them): –Arithmetic, logarithms, sets, graphs –Symbolic logic, implication –Proof techniques (induction, contradiction) The textbook is quite mathematical – you may need to read things more than once

23 UVa CS216 Spring Lecture 1: Analyzing Algorithms Expectations: Honor Everyone will be expected to follow what is on the course pledge Exact content will be determined before next class based on your survey responses –I hope to place a large burden on the honor system, but won’t if students think this puts honest students at a disadvantage

24 UVa CS216 Spring Lecture 1: Analyzing Algorithms Course Goals

25 UVa CS216 Spring Lecture 1: Analyzing Algorithms Course Goal 1 Learn to write delightful programs. correct, readable, elegant, economical, efficient, scalable, maintainable, secure, dependable

26 UVa CS216 Spring Lecture 1: Analyzing Algorithms Course Goal 2 Be able to predict how decisions about data representation will impact properties of an implementation. running time, memory use, ease of implementation, scalability, …

27 UVa CS216 Spring Lecture 1: Analyzing Algorithms Course Goal 3 Understand how a program executes at levels of abstraction ranging from a high-level programming language to machine memory. We will talk about what this means in Monday’s class.

28 UVa CS216 Spring Lecture 1: Analyzing Algorithms if U or V is empty U, V is the best alignment otherwise, Try three possibilities: 1. First elements of U and V are aligned: score of best alignments of U[1:] and V[1:] + c if U[0] == V[0] 2. First element of U is aligned with a gap in V score of best alignments of U[1:] and V + g 3. First element of V is aligned with a gap in U score of best alignments of U and V[1:] + g Pick the choice with the highest score Is this a “good” solution?

29 UVa CS216 Spring Lecture 1: Analyzing Algorithms Algorithm Properties Implementable – can be readily expressed as a program Termination – always finishes Correctness – always gives the correct answer Efficient – uses resources wisely Note: Chapter 2 of text has a similar list but separates “Implementable” into Effectiveness and Program Complexity

30 UVa CS216 Spring Lecture 1: Analyzing Algorithms Is it Implementable? def bestAlignment (U, V, c, g): if len(U) == 0 or len(V) == 0: return U, V else: (U0, V0) = bestAlignment (U[1:], V[1:], c, g) scoreNoGap = goodnessScore (U0, V0, c, g) if U[0] == V[0]: scoreNoGap += c # try inserting a gap in U (no match for V[0]) (U1, V1) = bestAlignment (U, V[1:], c, g) scoreGapU = goodnessScore (U1, V1, c, g) - g # try inserting a gap in V (no match for U[0]) (U2, V2) = bestAlignment (U[1:], V, c, g) scoreGapV = goodnessScore (U2, V2, c, g) - g …

31 UVa CS216 Spring Lecture 1: Analyzing Algorithms Is it Implementable? def bestAlignment (U, V, c, g): if len(U) == 0 or len(V) == 0: return U, V else: (U0, V0) = bestAlignment (U[1:], V[1:], c, g) scoreNoGap = goodnessScore (U0, V0, c, g) if U[0] == V[0]: scoreNoGap += c # try inserting a gap in U (no match for V[0]) (U1, V1) = bestAlignment (U, V[1:], c, g) scoreGapU = goodnessScore (U1, V1, c, g) - g # try inserting a gap in V (no match for U[0]) (U2, V2) = bestAlignment (U[1:], V, c, g) scoreGapV = goodnessScore (U2, V2, c, g) - g if scoreNoGap >= scoreGapU and scoreNoGap >= scoreGapV: return U[0] + U0, V[0] + V0 elif scoreGapU >= scoreGapV: return GAP + U1, V[0] + V1 else: return U[0] + U2, GAP + V2

32 UVa CS216 Spring Lecture 1: Analyzing Algorithms Algorithm Properties Implementable – can be readily expressed as a program Termination – always finishes Correctness – always gives the correct answer Efficient – uses resources wisely

33 UVa CS216 Spring Lecture 1: Analyzing Algorithms Termination? if U or V is empty U, V is the best alignment otherwise, Try three possibilities: 1. First elements of U and V are aligned: score of best alignments of U[1:] and V[1:] + c if U[0] == V[0] 2. First element of U is aligned with a gap in V score of best alignments of U[1:] and V + g 3. First element of V is aligned with a gap in U score of best alignments of U and V[1:] + g Pick the choice with the highest score

34 UVa CS216 Spring Lecture 1: Analyzing Algorithms if U or V is empty U, V is the best alignment otherwise, Try three possibilities: 1. First elements of U and V are aligned: score of best alignments of U[1:] and V[1:] + c if U[0] == V[0] 2. First element of U is aligned with a gap in V score of best alignments of U[1:] and V + g 3. First element of V is aligned with a gap in U score of best alignments of U and V[1:] + g Pick the choice with the highest score Every attempt, at least one element is removed (and none added). Initial length is finite, so must terminate.

35 UVa CS216 Spring Lecture 1: Analyzing Algorithms Algorithm Properties Implementable – can be readily expressed as a program Termination – always finishes Correctness – always gives the correct answer –Very informally: it tries all possibilities and picks the best one Efficient – uses resources wisely

36 UVa CS216 Spring Lecture 1: Analyzing Algorithms Efficiency? What resources do we care about? –Programmer Time –Running Time –Space Use

37 UVa CS216 Spring Lecture 1: Analyzing Algorithms Measuring Resource Use Space –Fundamental unit: bit Running Time –No fundamental unit Number of steps? How much can you do in one step? How long does a step take? How does it scale with the size of the input Answering for this algorithm is a PS1 question

38 UVa CS216 Spring Lecture 1: Analyzing Algorithms Charge Registration Survey –Linked from course web site –Submit by Friday 5pm Text: Read chapters 1-3 PS1: Out now, due in 1 week –Start now – the section time is not for doing PSs Monday: Levels of Abstraction, Order Notation